Constructing theoretical system for high-dimension, low-sample-size data

我们提出了高维低样本量（HDLSS）数据的统计理论和方法。我们发现HDLSS数据有两种不同的几何表示。我们提出了由几何表示带来的降噪方法。对于高维数据分析中出现的参数，我们提出了扩展的交叉数据矩阵方法，它提供了一个具有小渐近方差和低计算成本的无偏估计。我们提供了两种有效的判别方法：基于距离的分类器和几何分类器，可以确保错误分类率的高准确性，并将错误分类率保持在阈值以下。

We proposed statistical theories and methodologies for high-dimension, low-sample-size (HDLSS) data. We showed that HDLSS data have two distinct geometric representations. We proposed the noise-reduction methodology that was brought from the geometric representations. We proposed the extended Cross-data-matrix methodology, which offers an unbiased estimator having small asymptotic variance and low computational cost, for parameters appearing in high-dimensional data analysis. We provided two effective discriminant procedures: a distance-based classifier and a geometric classifier, which can ensure high accuracy in misclassification rates and hold misclassification rates less than a threshold.